Method and device for space-time estimation of one or more transmitters

ABSTRACT

Method and device for space-time estimation of one or more transmitters based on signals received using an antenna network. Signals received using the antenna network are separated in order to obtain signals s(t). Signals s(t) are grouped by transmitter, where the signals s(t) are from more than one transmitter, and arrival angles θ mi  of the multipaths p m  transmitted by each transmitter are determined.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention concerns a method for the space-time estimation of one ormore transmitters in an antenna network when the wave transmitted by atransmitter is propagated as multipaths.

Multipaths exist when a wave transmitted by a transmitter is propagatedalong several paths towards a receiver or a goniometry system.Multipaths are due in particular to the presence of obstacles between atransmitter and a receiver.

The field of the invention concerns in particular that of the goniometryof radioelectric sources, the word source designating a transmitter.Goniometry means “the estimation of incidences”.

It is also that of spatial filtering whose purpose is to synthesise anantenna in the direction of each transmitter from a network of antennas.

2. Discussion of the Background

The purpose of a traditional radiogoniometry system is to estimate theincidence of a transmitter, i.e. the angles of arrival of radioelectricwaves incident on a network 1 of N sensors of a reception system 2, forexample a network of several antennas as represented in FIGS. 1 and 2.The network of N sensors is coupled to a computation device 4 via Nreceivers in order to estimate the angles of incidence θ_(p) of theradioelectric waves transmitted by various sources p or transmitters andwhich are received by the network.

The wave transmitted by the transmitter can propagate along severalpaths according to a diagram given in FIG. 3. The wave k(θ_(d)) has adirect path with angle of incidence θ_(d) and the wave k(θ_(r)) areflected path with angle of incidence θ_(r). The multipaths are due inparticular to obstacles 5 located between the transmitter 6 and thereception system 7. At the reception station, the various paths arrivewith various angles of incidence θ_(op) where p corresponds to thep^(th) path. The multipaths follow different propagation routes and aretherefore received at different times t_(mp).

The N antennas of the reception system receive the signal x_(n)(t) wheren is the index of the sensor. Using these N signals x_(n)(t), theobservation vector is built: $\begin{matrix}{{\underset{\_}{x}(t)} = \begin{bmatrix}{x_{1}(t)} \\. \\. \\{x_{n}(t)}\end{bmatrix}} & (1)\end{matrix}$

With M transmitters this observation vector x(t) is written as follows:$\begin{matrix}{{\underset{\_}{x}(t)} = {{\sum\limits_{m = 1}^{M}{\sum\limits_{p = 1}^{P_{m}}{\rho_{mp}{\underset{\_}{a}\left( \theta_{mp} \right)}{s_{m}\left( {t - \tau_{mp}} \right)}}}} + {\underset{\_}{b}(t)}}} & (2)\end{matrix}$

where

a(θ_(mp)) is the steering vector of the p^(th) path of the m^(th)transmitter. The vector a(θ) is the response of the network of N sensorsto a source of incidence θ

ρ_(mp) is the attenuation factor of the p^(th) path of the m^(th)transmitter

τ_(mp) is the delay of the p^(th) path of the m^(th) transmitter

P_(m) is the number of multipaths of the m^(th) transmitter

s_(m)(t) is the signal transmitted by the m^(th) transmitter

b(t) is the noise vector composed of the additive noise b_(n)(t) (1≦n≦N)on each sensor.

The prior art describes various techniques of goniometry, of sourceseparation and of goniometry after the separation of the source.

These techniques consist of estimating the signals s_(m)(t−τ_(mp)) fromthe observation vector x(t) with no knowledge of their time properties.These techniques are known as blind techniques. The only assumption isthat the signals s_(m)(t−τ_(mp)) are statistically independent for apath p such that 1≦p≦P_(m) and for a transmitter m such that 1≦m≦M.Knowing that the correlation between the signals s_(m)(t) and s_(m)(t−τ)is equal to order 2 to the autocorrelation functionr_(sm)(τ)=E[s_(m)(t)s_(m)(t−τ)*] of the signal s_(m)(t), we deduce thatthe multipaths of a given signal s_(m)(t) transmitter are dependentsince the function r_(sm)(τ) is non null. However, two differenttransmitters m and m′, of respective signals s_(m)(t) and s_(m′)(t), arestatistically independent if the relation E[s_(m)(t) s_(m′)(t)*]=0 issatisfied, where E[.] is the expected value. Under these conditions,these techniques can be used when the wave propagates in a single path,when P₁= . . . =P_(M)=1. The observation vector x(t) is then expressedby: $\begin{matrix}{{\underset{\_}{x}(t)} = {{{\sum\limits_{m = 1}^{M}{{\underset{\_}{a}\left( \theta_{m} \right)}{s_{m}(t)}}} + {\underset{\_}{b}(t)}} = {{A\quad {\underset{\_}{s}(t)}} + {\underset{\_}{b}(t)}}}} & (3)\end{matrix}$

where A=[a(θ₁) . . . a(θ_(M))] is the matrix of steering vectors of thesources and s(t) is the source vector such that s(t)=[s₁(t) . . .s_(M)(t)]^(T) (where the exponent T designates the transpose of vector uwhich satisfies in this case u=s(t)).

These methods consist of building a matrix W of dimension (N×M), calledseparator, generating at each time t a vector y(t) of dimension M whichcorresponds to a diagonal matrix and, to within one permutation matrix,to an estimate of the source vector s(t) of the envelopes of the Msignals of interest to the receiver. This problem of source separationcan be summarised by the following expression of the required vectorialoutput at time t of the linear separator W:

y(t)=W ^(H) x(t)=ΠΛŝ(t)  (4)

where Π and Λ correspond respectively to arbitrary permutation anddiagonal matrices of dimension M and where ŝ(t) is an estimate of thevector s(t). W^(H) designates the transposition and conjugationoperation of the matrix W.

These methods involve the statistics of order 2 and 4 of the observationvector x(t).

Order 2 Statistics: Covariance Matrix

The correlation matrix of the signal x(t) is defined by the followingexpression:

R _(xx) =E[x(t)x(t)^(H)]  (5)

Knowing that the source vector s(t) is independent of the noise b(t) wededuce from (3) that:

R _(xx) =AR _(ss) A ^(H)+σ² I  (6)

Where R_(ss)=E[s(t) s(t)^(H)] and E[b(t) b(t)^(H)]=σ²I.

The estimate of R_(xx) used is such that: $\begin{matrix}{{\hat{R}}_{xx} = {\frac{1}{T}{\sum\limits_{t = 1}^{T}{{\underset{\_}{x}(t)}{\underset{\_}{x}(t)}^{H}}}}} & (7)\end{matrix}$

where T corresponds to the integration period.

Order 4 Statistics: Quadricovariance

By extension of the correlation matrix, we define with order 4 thequadricovariance whose elements are the cumulants of the sensor signalsx_(n)(t):

Qxx(i,j,k,l)=cum{xi(t), xj(t)*, xk(t)*, xl(t)}  (8) $\begin{matrix}\begin{matrix}{{{With}\quad {cum}\left\{ {y_{i},y_{j},y_{k},y_{i}} \right\}} = {{E\left\lbrack {y_{i}\quad y_{j}\quad y_{k}\quad y_{l}} \right\rbrack} - \quad {{E\left\lbrack {y_{i}\quad y_{j}} \right\rbrack}\left\lbrack {y_{k}\quad y_{l}} \right\rbrack}}} \\{- \quad {{E\left\lbrack {y_{i}\quad y_{k}} \right\rbrack}\left\lbrack {y_{j}\quad y_{l}} \right\rbrack}} \\{- \quad {{E\left\lbrack {y_{i}\quad y_{l}} \right\rbrack}\left\lbrack {y_{j}\quad y_{k}} \right\rbrack}}\end{matrix} & (9)\end{matrix}$

Knowing that N is the number of sensors, the elements Q_(xx)(i,j,k,l)are stored in a matrix Q_(xx) at line number N(j−1)+i and column numberN(l−1)+k. Q_(xx) is therefore a matrix of dimension N²×N².

It is also possible to write the quadricovariance of observations x(t)using the quadricovariances of the sources and the noise writtenrespectively Q_(ss) and Q_(bb). Thus according to expression (3) weobtain: $\begin{matrix}{Q_{xx} = {{\sum\limits_{i,j,k,l}{{{Q_{ss}\left( {i,j,k,l} \right)}\left\lbrack {{\underset{\_}{a}\left( \theta_{i} \right)} \otimes {\underset{\_}{a}\left( \theta_{j} \right)}^{*}} \right\rbrack}\left\lbrack {{\underset{\_}{a}\left( \theta_{k} \right)} \otimes {\underset{\_}{a}\left( \theta_{l} \right)}^{*}} \right\rbrack}^{H}} + Q_{bb}}} & (10)\end{matrix}$

where {circle around (x)} designates the Kronecker product such that:$\begin{matrix}{{\underset{\_}{u} \otimes \underset{\_}{v}} = {{\begin{bmatrix}{\underset{\_}{u}\quad v_{1}} \\. \\{\underset{\_}{u}\quad v_{K}}\end{bmatrix}\quad {where}\quad \underset{\_}{v}} = \begin{bmatrix}v_{1} \\. \\v_{K}\end{bmatrix}}} & (11)\end{matrix}$

Note that when there are independent sources, the following equality(12) is obtained:$Q_{xx} = {{\sum\limits_{m = 1}^{M}{{{Q_{ss}\left( {m,m,m,m} \right)}\quad\left\lbrack {\underset{\_}{a}{\left( \theta_{m} \right) \otimes {\underset{\_}{a}\left( \theta_{m} \right)}^{*}}} \right\rbrack}\quad\left\lbrack {\underset{\_}{a}{\left( \theta_{m} \right) \otimes {\underset{\_}{a}\left( \theta_{m} \right)}^{*}}} \right\rbrack}^{H}} + Q_{bb}}$

Since Q_(ss)(i,j,k,l)=0 for i≠j≠k≠l. In addition, in the presence ofGaussian noise the quadricovariance Q_(bb) of the noise cancels out andleads to (13):$Q_{xx} = {\sum\limits_{m = 1}^{M}{{{Q_{ss}\left( {m,m,m,m} \right)}\quad\left\lbrack {\underset{\_}{a}{\left( \theta_{m} \right) \otimes {\underset{\_}{a}\left( \theta_{m} \right)}^{*}}} \right\rbrack}\quad\left\lbrack {\underset{\_}{a}{\left( \theta_{m} \right) \otimes {\underset{\_}{a}\left( \theta_{m} \right)}^{*}}} \right\rbrack}^{H}}$

An example of a known source separation method is the Souloumiac-Cardosomethod which is described, for example, in document [1] entitled “BlindBeamforming for Non Gaussian Signals”, authors J. F. CARDOSO, A.SOULOUMIAC, published in the review IEE Proc-F, Vol 140, No. 6, pp362-370, December 1993.

FIG. 4 schematises the principle of this separation method based on thestatistical independence of sources. Under these conditions, thematrices R_(ss) and Q_(ss) of expressions (6) and (10) are diagonal.This figure shows that the algorithm used to process the observationvector corresponding to the signals received on the sensor network iscomposed of a data x(t) whitening step 10 resulting in an observationvector z(t), and a steering vector identification step 11, possiblyfollowed by a spatial filtering step 12 using the signal vector x(t) toobtain an estimated signal ŝ′(t). The whitening step uses the covariancematrix R_(xx) in order to orthonormalise the basis of the steeringvectors a(θ₁) . . . a(θ_(M)). The second identification step uses thequadricovariance Q_(zz) to identify the steering vectors previouslyorthonormalised.

The coefficients of the spatial filtering step W_(i) are defined asfollows

w _(i) =aR _(x) ⁻¹ a(θ_(i))

Whitening Step

Whitening is carried out to orthogonalise the mixture matrix A to beestimated. The observations x(t) must be multiplied by a matrix Θ⁻¹ suchthat the covariance matrix of denoised and whitened observations isequal to the identity matrix. z(t) represents the vector of noised andwhitened observations:

z(t)=Θ⁻¹ x(t)=Θ⁻¹ As(t)+Θ⁻¹ b(t)  (14)

The matrix Θ of dimension N×M must then satisfy according to (6) thefollowing relation:

ΘΘ^(H) =R _(xx) −R _(bb) =AR _(ss) A ^(H)  (15)

Knowing that E[b(t) b(t)^(H)]=σ² I, we deduce from (6) that thedecomposition into eigenelements of R_(xx) satisfies:

R _(xx) =E _(s)Λ_(s) E _(s) ^(H)+σ² E _(b) E _(b) ^(H)  (16)

Where Λ_(s) is a diagonal matrix of dimension M×M containing the Mlargest eigenvalues of R_(xx). The matrix E_(s) of dimension N×M iscomposed of eigenvectors associated with the largest eigenvalues ofR_(xx) and the matrix E_(b) of dimension N×(N−M) is composed ofeigenvectors associated with the noise eigenvalue σ². Knowing firstlythat R_(bb)=E[b(t) b(t)^(H)]=σ² I and that secondly by definition fromthe decomposition into eigenelements that (E_(s) E_(s) ^(H+E) _(b) E_(b)^(H))=I, we deduce from (15) that:

ΘΘ^(H) =A R _(ss) A ^(H) =E _(s)(Λ_(s)−σ² I _(M))E _(s) ^(H)  (17)

We can then take for matrix Θ the following matrix of dimension N×M.

Θ=E _(s)(Λ_(s)−σ² I _(M))^(½)  (18)

According to (17) we deduce that the matrix Θ also equals:

Θ=A R _(ss) ^(½) U ^(H) with U ^(H) U=I _(M)  (19)

U is then a unit matrix whose columns are formed from orthonormedvectors. According to (3), (14) and (19) the vector z(t) of dimensionM×1 can be expressed as follows:

z(t)=Us′(t)+Θ⁻¹ b(t) with s′(t)=R _(ss) ^(−½) s(t)  (20)

With decorrelated sources, the matrices R_(ss) and R_(ss) ^(−½) arediagonal and so the components of vectors s′(t) and s(t) are equal towithin one amplitude such that:${{\underset{\_}{s}}^{\prime}(t)} = {{\begin{bmatrix}{{s_{1}(t)}/\sqrt{\gamma_{1}}} \\. \\{{s_{M}(t)}/\sqrt{\gamma_{M}}}\end{bmatrix}\quad {where}\quad {\underset{\_}{s}(t)}} = {{\begin{bmatrix}{s_{1}(t)} \\. \\{s_{M}(t)}\end{bmatrix}\quad {and}\quad R_{ss}} = \begin{bmatrix}\gamma_{1} & . & 0 \\. & . & . \\0 & . & \gamma_{M}\end{bmatrix}}}$

The matrix U is composed of whitened steering vectors such that:

U=[t _(l) . . . t _(M)]  (21)

Identification Step

The purpose of this step is to identify the unit matrix U composed of Mwhitened steering vectors t_(m). According to (20) and (21), the vectorz(t) of whitened observations can be expressed as follows:$\begin{matrix}{{{\underset{\_}{z}(t)} = {{{U\quad {{\underset{\_}{s}}^{\prime}(t)}} + {\Theta^{- 1}{\underset{\_}{b}(t)}}} = {{\sum\limits_{m = 1}^{M}{{\underset{\_}{t}}_{M}{s_{m}^{\prime}(t)}}} + {{\underset{\_}{b}}^{\prime}(t)}}}}{\text{with}\quad {s_{m}^{\prime}(t)}} = {{{{s_{m}(t)}/\sqrt{\gamma_{m}}}\quad \text{and}\quad {{\underset{\_}{b}}^{\prime}(t)}} = {\Theta^{- 1}{{\underset{\_}{b}(t)}.}}}} & (22)\end{matrix}$

Knowing that the M signal sources s′_(m)(t) are independent, we deduceaccording to (13) that the quadricovariance of z(t) can be written asfollows: $\begin{matrix}{Q_{zz} = {\sum\limits_{m = 1}^{M}{{{Q_{s^{\prime}s^{\prime}}\left( {m,m,m,m} \right)}\left\lbrack {{\underset{\_}{t}}_{m} \otimes {\underset{\_}{t}}_{m}^{*}} \right\rbrack}\left\lbrack {{\underset{\_}{t}}_{m} \otimes {\underset{\_}{t}}_{m}^{*}} \right\rbrack}^{H}}} & (23)\end{matrix}$

Under these conditions, the matrix Q_(zz) of dimension M²×M² has rank M.Diagonalisation of Q_(zz) then enables us to retrieve the eigenvectorsassociated with the M largest eigenvalues. These eigenvectors can bewritten as follows: $\begin{matrix}{{\underset{\_}{e}}_{m} = {{\sum\limits_{i = 1}^{M}{{\alpha_{mi}\left( {{\underset{\_}{t}}_{i} \otimes {\underset{\_}{t}}_{i}^{*}} \right)}\quad \text{for}\quad m}} = {1\quad \cdots \quad M}}} & (24)\end{matrix}$

We then transform each vector e_(m) of length M² into a matrix U_(m) ofdimension (M×M) whose columns are the M M-uplets forming, the vectore_(m). $\begin{matrix}{{U_{m} = \begin{pmatrix}e_{m,1} & e_{m,{M + 1}} & \cdots & e_{m,{{{({M - 1})}M} + 1}} \\\vdots & \vdots & \vdots & \vdots \\e_{m,M} & e_{m,{2M}} & \cdots & e_{m,M^{2}}\end{pmatrix}}{{\text{with}\quad {\underset{\_}{e}}_{m}} = \begin{pmatrix}e_{m,1} \\\vdots \\e_{m,M} \\\vdots \\e_{m,{{{({M - 1})}M} + 1}} \\\vdots \\e_{\overset{.}{m},M^{2}}\end{pmatrix}}} & (25)\end{matrix}$

which according to equation (24) can also be written: $\begin{matrix}{U_{m} = {{\sum\limits_{i = 1}^{M}{\alpha_{mi}{\underset{\_}{t}}_{i}{\underset{\_}{t}}_{i}^{H}}} = {U\quad \delta_{m}U^{H}}}} & (26)\end{matrix}$

where δ_(m) is a diagonal matrix of elements α_(mi). To identify thematrix U, simply diagonalise the eigenmatrices U_(m) for 1≦m≦M since thematrix U is a unit matrix due to the whitening step. Reference [1]proposes an algorithm for joint diagonalisation of the M matrices U_(m).

Knowing the matrices U and Θ we can deduce according to (19) the matrixA of steering vectors such that:

ΘU=A R _(ss) ^(½) =[a′ _(l) . . . a′ _(M)] with a′ _(m)=a(θ_(m))×{square root over (γ_(m))}  (27)

We therefore identify the steering vectors a(θ_(m)) of the sources towithin a multiplying factor {square root over (γ_(m))}. According toexpressions (20) and (14) and knowing the matrices U and Θ we deduce theestimate of the source vector s′(t) such that:${{\underset{\_}{\hat{s}}}^{\prime}(t)} = {U^{H}\Theta^{- 1}{\underset{\_}{x}(t)}}$${\text{where}\quad {{\underset{\_}{\hat{s}}}^{\prime}(t)}} = \begin{bmatrix}{{{\hat{s}}_{1}(t)}/\sqrt{\gamma_{1}}} \\\vdots \\{{{\hat{s}}_{M}(t)}/\sqrt{\gamma_{M}}}\end{bmatrix}$

knowing that $\begin{matrix}{R_{ss} = \begin{bmatrix}\gamma_{1} & \cdots & 0 \\\vdots & \vdots & \vdots \\0 & \cdots & \gamma_{M}\end{bmatrix}} & (28)\end{matrix}$

We therefore estimate the signals s_(m)(t) to within a multiplyingfactor of value (1/{square root over (γ_(m))}) such that:

ŝ′ _(m)(t)=(1/{square root over (γ_(m))}) ŝ _(m)(t)  (29)

Behaviour with Multipaths

Knowing that, for a given transmitter m, the signals s_(m)(t) ands_(m)(t−τ) are correlated, it is possible to deduce the existence ofdependence between the signal multipaths s_(m)(t−τ_(mp)) with 1<p<P_(m).

It was demonstrated in reference [2], authors P. CHEVALIER, V.CAPDEVIELLE, P. COMON, entitled “Behaviour of HO blind source separationmethods in the presence of cyclostationary correlated multipaths”,published in the IEEE review SP Workshop on HOS, Alberta (Canada), July1997, that the source separation method separates the transmitterswithout separating their multipaths. So by taking the signal model ofexpression (2) for the m^(th) transmitter we identify the followingP_(m) vectors: $\begin{matrix}{{\underset{\_}{u}}_{mp} = {{\sum\limits_{i = 1}^{P_{m}}{\beta_{mpi}{\underset{\_}{a}\left( \theta_{mi} \right)}\quad \text{for}\quad 1}} \leq p \leq P_{m}}} & (30)\end{matrix}$

Similarly for the m^(th) transmitter we identify the following P_(m)signals: $\begin{matrix}{{{\hat{s}}_{mp}^{\prime}(t)} = {{\sum\limits_{i = 1}^{P_{m}}{\beta_{mpi}^{\prime}{{\hat{s}}_{m}\left( {t - \tau_{mi}} \right)}\quad \text{for}\quad 1}} \leq p \leq P_{m}}} & (31)\end{matrix}$

These source separation techniques assume, in order to be efficient,that the signals propagate in a single path. The signals transmitted byeach transmitter are considered as statistically independent.

With a single path where P₁= . . . =P_(m)=1, the sources are allindependent and the M vectors identified at separation output have,according to the relation (27), the following structure:

a′ _(m)=β_(m) a(θ_(m)) for 1≦m≦M  (32)

For each transmitter, the following noise projector Π_(bm) is built:$\begin{matrix}{\prod\limits_{bm}{= {{I_{N} - {\frac{{\underset{\_}{a}}_{m}^{\prime}{\underset{\_}{a}}_{m}^{\prime \quad H}}{{\underset{\_}{a}}_{m}^{\prime \quad H}{\underset{\_}{a}}_{m}^{\prime}}\quad \text{for}\quad 1}} \leq m \leq M}}} & (33)\end{matrix}$

By applying the MUSIC principle we then look for the incidence{circumflex over (θ)}_(m) of the m^(th) transmitter which cancels thefollowing criterion: $\begin{matrix}{{\hat{\theta}}_{m} = {{\begin{matrix}\min \\\theta\end{matrix}\left\{ {{\underset{\_}{a}(\theta)}^{H}{\prod\limits_{bm}{\underset{\_}{a}(\theta)}}} \right\} \quad \text{for}\quad 1} \leq m \leq M}} & (34)\end{matrix}$

The principle of the MUSIC algorithm is for example described indocument [3] by R. O. Schmidt entitled “A signal subspace approach tomultiple emitters location and spectral estimation”, PhD Thesis,Stanford University, CA, November 1981.

Thus, using vectors a′₁ . . . a′_(M) identified at source separationoutput it is possible to deduce the incidences {circumflex over (θ)}₁ .. . {circumflex over (θ)}_(M) for each transmitter. However, the sourcesmust be decorrelated if the vectors identified are to satisfy therelation a′_(m)=β_(m) a (θ_(m)).

For example, in document [4] entitled “Direction finding after blindidentification of sources steering vectors: The Blind-Maxcor andBlind-MUSIC methods”, authors P. CHEVALIER, G. BENOIT, A. FERREOL, andpublished in the review Proc. EUSIPCO, Triestre, September 1996, ablind-MUSIC algorithm of the same family as the MUSIC algorithm, knownby those skilled in the art, is applied.

The known techniques of the prior art can therefore be used to determinethe incidences for the various transmitters if the wave transmitted foreach of these transmitters propagates as monopath.

The invention concerns a method and a device which can be used todetermine in particular, for each transmitter propagating as multipaths,the incidences of the arrival angles for the multipaths.

SUMMARY OF THE INVENTION

The purpose of this invention is to carry out selective goniometry bytransmitter in the presence of multipaths, i.e. for P_(m)>1.

One of the methods implemented by the invention is to group the signalsreceived for each transmitter, before carrying out the goniometry of allthese multipaths for each transmitter, for example.

Another method consists of space-time separation of the sources ortransmitters.

In this description, the following terms are defined:

Ambiguities: we have an ambiguity when the goniometry algorithm canestimate with equal probability either the true incidence of the sourceor another quite different incidence. The greater the number of sourcesto be identified simultaneously, the greater the risk of ambiguity.

Multipath: when the wave transmitted by a transmitter propagates alongseveral paths towards the goniometry system. Multipaths are due to thepresence of obstacles between a transmitter and a receiver.

Blind: with no a priori knowledge of the transmitting sources.

The invention concerns a method for space-time estimation of the anglesof incidence of one or more transmitters in an antenna network whereinit comprises at least a step to separate the transmitters and a step todetermine the various arrival angles θ_(mi) of the multipaths ptransmitted by each transmitter.

According to a first mode of realisation, the method comprises at leasta step to separate the transmitters in order to obtain the varioussignals s(t) received by the antenna network, a step to group thevarious signals by transmitter and a step to determine the variousangles θ_(mi) of the multipaths by transmitter.

The step to group the various signals by transmitter comprises forexample:

a step to intercorrelate two by two the components u_(k)(t) of thesignal vector s′(t) resulting from the source separation step,

a step to find the delay value(s) in order to obtain a maximum value forthe intercorrelation function, r_(kk′)(τ)=E[u_(k)(t)u_(k′)(t−τ)*],

a step to store the various path indices for which the correlationfunction is a maximum.

The method comprises for example a step to determine delay times usingthe incidences θ_(mi), the signal s_(m)(t) and the search for themaximum of the criterion Cri_(i)(δτ) to obtain δτ_(mi)=τ_(mi)−τ_(ml),with Cri_(i)(δτ)=E[s_(m)(t)(i)s_(m)(t−δτ)(1)*].

According to a second realisation variant, the method comprises a stepof space-time separation of the various transmitters before determiningthe various arrival angles θ_(mi).

The space-time separation step comprises for example a step where, for agiven transmitter, the signal s_(m)(t) is delayed, thereby comparing thedelayed signal to the output of a filter of length L_(m), whose inputsare s_(m)(t) up to s_(m)(t−τ_(m)), before applying the sourceseparation.

The method may comprise a step to identify and eliminate the outputsassociated with the same transmitter after having determined the anglesθ_(mi).

The method implements, for example, different types of goniometry, suchas high resolution methods such as in particular MUSIC, interferometrymethods, etc.

The method applies to the goniometry of multipath sources and also whenP₁= . . . =P_(m)=1.

The invention also concerns a device to make a space-time estimation ofa set of transmitters which transmit waves propagating as multipaths ina network of N sensors wherein it comprises a computer designed toimplement the steps of the method characterised by the steps describedabove.

The method according to the invention can be used in particular to carryout separate goniometry of the transmitters. Thus, only the incidencesof the multipaths of a given transmitter are determined.

Under these conditions, compared with a traditional technique which mustsimultaneously locate all the transmitters with their multipaths, themethod can be used to perform goniometry on fewer sources.

BRIEF DESCRIPTION OF THE DRAWINGS

Other advantages and features of the invention will be clearer onreading the following description given as a non-limiting example, withreference to figures representing in:

FIG. 1 a transmission-reception system, and in FIG. 2 a network of Nsensors,

FIG. 3 the possible paths of waves transmitted by a transmitter,

FIG. 4 a source separation method according to the prior art,

FIG. 5 a diagram of the various steps of a first method according to theinvention of source association and in FIG. 6 the associated processingalgorithm,

FIG. 7 a second variant with space-time source separation,

FIG. 8 an example of the spectrum obtained.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The acquisition system described in FIG. 2 includes a network 2 composedof N antennas 3 ₁ to 3 _(N) linked to a computer 4 designed inparticular to implement the various steps of the method according to theinvention. The computer is for example adapted to determine the arrivalangles for each transmitter 1 i (FIG. 1) transmitting a wave which canpropagate as multipaths as shown on the diagram in FIG. 1. The computeris equipped with means to perform the goniometry of each transmitter 1i.

The sensors or antennas of the receiver system receive signals x_(n)(t)as described previously, so that the observation vector x(t) can bebuilt using the N antennas.

Remember that when there are multipaths, we identify for the m^(th)transmitter, P_(m) paths for the propagation of the transmitted wave andthe following P_(m) vectors:${\underset{\_}{u}}_{mp} = {{\sum\limits_{i = 1}^{P_{m}}{\beta_{mpi}{\underset{\_}{a}\left( \theta_{mi} \right)}\quad \text{for}\quad 1}} \leq p \leq P_{m}}$

where a(θ_(mi)) is the steering vector of the i^(th) path of the m^(th)transmitter.

Similarly for this m^(th) transmitter we identify the following P_(m)signals:${{\hat{s}}_{mp}^{\prime}(t)} = {{\sum\limits_{i = 1}^{P_{m}}{\beta_{mpi}^{\prime}{{\hat{s}}_{m}\left( {t - \tau_{mi}} \right)}\quad \text{for}\quad 1}} \leq p \leq P_{m}}$

Also, for paths p≠p′, the signals ŝ′_(mp)(t) and ŝ′_(mp′)(t) output froma separation step are independent since they satisfy:

E[ŝ′ _(mp)(t)ŝ′ _(mp′)(t)*]=0.

The idea of the method according to the invention is to carry outseparate goniometry of the transmitters when the wave or waves propagateas multipaths, either by grouping the various outputs by transmitter, orby introducing a space-time source separation step before performing thegoniometry for each transmitter.

Method Associating the Source Separation Outputs by Transmitter

According to a first implementation of the method described in FIG. 5,the invention consists of detecting the outputs ŝ′_(mp)(t) issued fromthe separation step 20, of grouping 21 the outputs belonging to the sametransmitter and of performing for example a goniometry step 22 on eachoutput, for a given transmitter.

The method includes for example the following steps:

a) Separate, 20, the sources according to a separation method known byProfessionals and applied to the observation vector x(t) received by theantenna network. After this separation step, the method has obtained avector s′(t) of components ŝ′_(mp)(t) representative of the variouspaths transmitted by the m^(th) transmitter,

b) Group the outputs by transmitter, 21,

c) Correlate two by two the components of the vector s′(t) resultingfrom the source separation step,

d) Search for the value of the delay time τ_(mp) to obtain a maximumvalue of the intercorrelated signals, and store the corresponding paths,for example in a table.

e) Perform a goniometry step, 22, for each transmitter to obtain theangles θ_(mPm)

Following the separation step a), the vector s′(t) of componentŝ′_(mp)(t) can be written as follows: $\begin{matrix}{{{\hat{\underset{\_}{s}}}^{\prime}(t)} = {{\begin{bmatrix}{u_{1}(t)} \\\vdots \\{u_{K}(t)}\end{bmatrix}\quad \text{where}\quad K} = {{\sum\limits_{m = 1}^{M}{P_{m}\quad \text{and}\quad {u_{k}(t)}}} = {{\hat{s}}_{mp}^{\prime}(t)}}}} & (35)\end{matrix}$

According to expression (31), the function r_(kk′)(τ) ofintercorrelation between the signals u_(k)(t) and u_(k′)(t) is non nullwhen they are associated with the same transmitter.

r _(kk′)(τ)=E[u _(k)(t)u _(k′)(t−τ)*]≠0 for τ>0 and k≠k′  (36)

The signals u_(k)(t) and u_(k′)(t) are in fact different linearcombinations of the signals ŝ_(m)(t−τ_(mp)) for (1≦p≦P_(m)). Knowingthat after filtering these two signals are noised respectively byb_(k)(t) et b_(k′)(t), we obtain:${u_{k}(t)} = {{\sum\limits_{i = 1}^{P_{m}}{\beta_{ki}^{\prime}{{\hat{s}}_{m}\left( {t - \tau_{mi}} \right)}}} + {b_{k}(t)}}$${u_{k^{\prime}}\left( {t - \tau} \right)} = {{\sum\limits_{i = 1}^{P_{m}}{\beta_{k^{\prime}i}^{\prime}{{\hat{s}}_{m}\left( {t - \tau_{mi} - \tau} \right)}}} + {b_{k^{\prime}}(t)}}$

The method comprises for example a step to search for the delay valuewhich maximises the intercorrelation between the outputs u_(k)(t) andu_(k′)(t−τ) and a step to store the indices k and k′ when the maximumexceeds a threshold.

To test the correlation between u_(k)(t) and u_(k′)(t−τ), a Gardner typedetection test can be applied, such as that described in the documententitled “Detection of the number of cyclostationary signals in unknowsinterference and noise”, authors S V. Schell and W. Gardner, publishedin Proc of Asilonan conf on signal, systems and computers 5-7 November90.

To do this, the following detection criterion can be calculated:$\begin{matrix}{{{{V_{{kk}^{\prime}}(\tau)} = {{- 2}T\quad {\ln \left( {1 - \frac{{{\hat{r}}_{{kk}^{\prime}}}^{2}}{{\hat{r}}_{kk}{\hat{r}}_{k^{\prime}k^{\prime}}}} \right)}}}{\text{with}\quad {\hat{r}}_{{kk}^{\prime}}} = {{\frac{1}{T}{\sum\limits_{t = 1}^{T}{{u_{k}(t)}{u_{k^{\prime}}\left( {t - \tau} \right)}^{*}\quad \text{and}\quad {\hat{r}}_{kk}}}} = {\frac{1}{T}{\sum\limits_{t = 1}^{T}{{u_{k}(t)}}^{2}}}}}{{\text{then}\quad {\hat{r}}_{k^{\prime}k^{\prime}}} = {\frac{1}{T}{\sum\limits_{t = 1}^{T}{{u_{k^{\prime}}\left( {t - \tau} \right)}}^{2}}}}} & (37)\end{matrix}$

Knowing that in the assumption where u_(k)(t)=b_(k)(t) andu_(k′)(t)=b_(k′)(t) the criterion V_(kk′)(τ) obeys a chi-2 law with 2degrees of freedom, we deduce the correlation test by defining athreshold α(pfa):

The signals u_(k)(t) and u_(k′)(t) are correlated (H₁):V_(kk′)(τ)>α(pfa)

The signals u_(k)(t) and u_(k′)(t) are decorrelated (H₀):V_(kk′)(τ)<α(pfa)

Knowing the probability law of the criterion V_(kk′)(τ) with noise onlyassumption, we then choose the threshold α(pfa) in a chi-2 table for aprobability of exceeding a given threshold, with 2 degrees of freedom.

FIG. 6 summarises an example of implementing the grouping techniqueincluding the correlation test.

For a transmitter of given index m, the computer searches for the delayvalues τ for which the energy received by the antenna network is amaximum, by making a two by two intercorrelation of the signalsresulting from the separation of sources 30, 31, 32, functionr_(kk′)(τ). It stores the chosen paths, maximising the intercorrelationfunction, in a table Tk containing the indices of the chosen paths andthe indices of the transmitters, 33, by using the above-mentionedcorrelation test and the threshold α(pfa), 34. Then the methodeliminates the identical tables Tk, for example by simple comparison 35.The computer then determines the table Tm(p), 36, composed of the sourceseparation output indices associated with the same transmitter.Following these steps, the computer can perform goniometry for eachtransmitter.

Following these steps, the computer determines the number M oftransmitters and the number of paths Pm for each transmitter. The tableTm obtained contains the source separation output indices associatedwith the same transmitter.

Goniometry

Knowing the paths for each transmitter, the computer carries out, forexample, a goniometry for each transmitter as described below.

For a transmitter composed of P_(m) paths we know, according toexpression (30), that the P_(m) vectors identified further to sourceseparation are all a linear combination of steering vectors a(θ_(mi)) ofits multipaths.${\underset{\_}{u}}_{k} = {{{\sum\limits_{i = 1}^{P_{m}}{\beta_{ki}{\underset{\_}{a}\left( \theta_{mi} \right)}\quad \text{for}\quad 1}} \leq p \leq {P_{m}\quad \text{knowing~~that}\quad {T_{m}(p)}}} = k}$

The table T_(m)(p) is composed of the source separation output indicesassociated with the same transmitter. With the P_(m) outputs u_(k) wetherefore calculate the following covariance matrix: $\begin{matrix}{R_{xm} = {\frac{1}{P_{m}}{\sum\limits_{p = 1}^{P_{m}}{{\underset{\_}{u}}_{{Tm}{(p)}}{\underset{\_}{u}}_{{Tm}{(p)}}^{H}}}}} & (38)\end{matrix}$

To estimate the incidences of the multipaths θ_(ml) up to θ_(mPm),simply apply any goniometry algorithm on the covariance matrix R_(xm).In particular, we can apply a high resolution algorithm such as MUSICdescribed in reference [3]. Note that the blind-MUSIC algorithm ofreference [4] is a special case of the latter algorithm when MUSIC isapplied with P_(m)=1.

Estimation of the Delay Times of the Paths of the m^(th) Transmitter

According to an implementation variant of the invention, the methodestimates the values of the delay times of the paths of the m^(th)transmitter.

In this paragraph, the incidences θ_(mi) of the P_(m) paths are assumedknown for 1<i<P_(m), and the associated steering vectors a(θ_(mi))deduced from these values. This information is used by the method todeduce the propagation delays between the various paths. We know thatthe vectors u_(mi) and the signals ŝ′_(mp)(t) obtained at sourceseparation output satisfy the following relation: $\begin{matrix}{{\sum\limits_{i = 1}^{P_{m}}{\rho_{mi}{\underset{\_}{a}\left( \theta_{mi} \right)}{s_{m}\left( {t - \tau_{mi}} \right)}}} = {\sum\limits_{i = 1}^{P_{m}}{{\underset{\_}{u}}_{mi}{{\hat{s}}_{mi}^{\prime}(t)}}}} & (40)\end{matrix}$

where ρ_(mi) designates the attenuation factor of the i^(th) path.Expression (40) can be written in matrix form as follows:

A _(m) s _(m)(t)=U _(m) ŝ′ _(m)(t)  (41)

By putting: A_(m)=[a(θ_(ml)) . . . a(θ_(mPm))] and U_(m)=[u_(ml) . . .u_(mPm)] and ${{\underset{\_}{s}}_{m}(t)} = {{\begin{bmatrix}{\rho_{m1}{s_{m}\left( {t - \tau_{m1}} \right)}} \\\vdots \\{\rho_{mPm}{s_{m}\left( {t - \tau_{mPm}} \right)}}\end{bmatrix}\quad \text{then}\quad {{\hat{\underset{\_}{s}}}_{m}^{\prime}(t)}} = \begin{bmatrix}{{\hat{s}}_{m1}(t)} \\\vdots \\{{\hat{s}}_{mPm}(t)}\end{bmatrix}}$

Knowing the matrix A_(m) of steering vectors of the multipaths and thematrix U_(m) of vectors identified, we deduce the vector s_(m)(t)according to the vector ŝ′_(m)(t) resulting from the source separationsuch that:

s _(m)(t)=A _(m) ⁻¹ U _(m) ŝ′ _(m)(t)  (42)

Knowing that the i^(th) component of s_(m)(t) satisfiess_(m)(t)(i)=ρ_(mi) s_(m)(t−τ_(mi)) we maximise the following criterionto estimate the delay δτ_(mi)=τ_(mi)−τ_(ml) of the i^(th) path withrespect to the 1^(st) path. $\begin{matrix}{{{Cri}_{i}\left( {\delta \quad \tau} \right)} = {{{E\left\lbrack {{s_{m}(t)}(i){s_{m}\left( {t - {\delta \quad \tau}} \right)}(1)^{*}} \right\rbrack}\quad \text{such~~~that}\quad \max \quad \left( {{Cri}\left( {\underset{\delta \quad \tau}{\delta}\quad \tau} \right)} \right)} = {\delta \quad \tau_{m\quad i}}}} & (43)\end{matrix}$

The algorithm to estimate the δτ_(mi) for 1i<P_(m) consists ofperforming the following steps:

Step No. 1: Construct A_(m)=[a(θ_(ml)) . . . a(θ_(mPm))] from incidencesθ_(mi).

Step No. 2: Calculate the signal s_(m)(t) using the expression (42).

Step No. 3: For each path perform the following operations

Calculate the criterion Cri_(i)(δτ) of expression (43)

Maximise the criterion Cri_(i)(δτ) to obtain δτ_(mi)=τ_(mi)−τ_(ml).

Space-Time Source Separation

A second method to implement the invention consists for example ofapplying the source separation on the space-time observationy(t)=[x(t)^(T) . . . x(t−L+1)^(T)]^(T).

FIG. 7 represents an example of a diagram to execute the steps of themethod.

By using the space-time observation, it is possible to apply directly,on each source separation output, a goniometry of the multipaths of oneof the transmitters. Since one transmitter is associated with severaloutputs, the method includes a step to eliminate the outputs associatedwith the transmitter on which the goniometry process has just beencarried out.

This second realisation variant can be used in particular to locate moresources than with the first method. According to this second variant infact, the limiting parameter is the number of transmitters (M<N) whereaspreviously, the limiting parameter is the total number of multipaths,i.e. ΣP_(m)<N.

In this second implementation variant, the signal model used is that ofexpression (2). Firstly, the method includes a step 40 to model thesignals s_(m)(t) by considering them as finite pulse response signals oflength L_(m). Under these conditions, the delayed signal s_(m)(t−τ_(mp))is the output of a filter of length L_(m), whose inputs are s_(m)(t) upto s_(m)(t−L_(m)+1), i.e.: $\begin{matrix}{{s_{m}\left( {t - \tau_{mp}} \right)} = {\sum\limits_{k = 1}^{L_{m}}{{h_{mp}(k)}{s_{m}\left( {t - k + 1} \right)}}}} & (44)\end{matrix}$

By taking expression (2) again, we obtain the following expression forx(t): $\begin{matrix}{{{\underset{\_}{x}(t)} = {{\sum\limits_{m = 1}^{M}{\sum\limits_{k = 1}^{L_{m}}{{{\underset{\_}{h}}_{m}(k)}{s_{m}\left( {t - k} \right)}}}} + {\underset{\_}{b}(t)}}}{{\text{with}\quad {{\underset{\_}{h}}_{m}(k)}} = {\sum\limits_{p = 1}^{P_{m}}{\rho_{mp}{\underset{\_}{a}\left( \theta_{mp} \right)}{h_{mp}(k)}}}}} & (45)\end{matrix}$

The space-time observation y(t) associated with x(t) can be written asfollows (46): ${\underset{\_}{y}(t)} = {\begin{bmatrix}{\underset{\_}{x}(t)} \\\vdots \\{\underset{\_}{x}\left( {t - L + 1} \right)}\end{bmatrix} = {{\sum\limits_{m = 1}^{M}{\sum\limits_{k = 1}^{L_{m} + L}{{{\underset{\_}{h}}_{m}^{L}(k)}{s_{m}\left( {t - k} \right)}}}} + {{\underset{\_}{b}}^{L}(t)}}}$${\text{with}\quad {{\underset{\_}{b}}^{L}(t)}} = \begin{bmatrix}{\underset{\_}{b}(t)} \\\vdots \\{\underset{\_}{b}\left( {t - L + 1} \right)}\end{bmatrix}$

Knowing that:${\underset{\_}{x}\left( {t - 1} \right)} = {{\sum\limits_{m = 1}^{M}{\sum\limits_{k = {1 + l}}^{L_{m} + l}{{{\underset{\_}{h}}_{m}\left( {k - l} \right)}{s_{m}\left( {t - k} \right)}}}} + {\underset{\_}{b}(t)}}$

Ignoring the edge effects, we deduce that: $\begin{matrix}{{{\underset{\_}{h}}_{m}^{L}(k)} = {\begin{bmatrix}{{\underset{\_}{h}}_{m}(k)} \\\vdots \\{\underset{\_}{h}\left( {k - L + 1} \right)}\end{bmatrix} = {\sum\limits_{p = 1}^{P_{m}}{\rho_{mp}\begin{bmatrix}{{\underset{\_}{a}\left( \theta_{mp} \right)}{h_{mp}(k)}} \\\vdots \\{{\underset{\_}{a}\left( \theta_{mp} \right)}{h_{mp}\left( {k - L + 1} \right)}}\end{bmatrix}}}}} & (47)\end{matrix}$

Source Separation and Goniometry on the Space-Time Observation y(t):

The method, for example, implements directly, 41, the Souloumiac-Cardososource separation method described in the afore-mentioned reference [1]on the observation vector y(t). Knowing that the signals s_(m)(t−k) arecorrelated, according to equations (46), (30) and reference [2], themethod identifies for each transmitter several space-time signaturesu_(mk) satisfying: $\begin{matrix}{{\underset{\_}{u}}_{mk} = {{\sum\limits_{i = 1}^{L_{m} + L}{\beta_{mki}{{\underset{\_}{h}}_{m}^{L}(i)}}} = {{\sum\limits_{p = 1}^{P_{m}}{\rho_{mp}{\sum\limits_{i = 1}^{L_{m} + L}{{\beta_{mki}\begin{bmatrix}{{\underset{\_}{a}\left( \theta_{mp} \right)}{h_{mp}(i)}} \\\vdots \\{{\underset{\_}{a}\left( \theta_{mp} \right)}{h_{mp}\left( {i - L + 1} \right)}}\end{bmatrix}}\quad 1}}}} \leq k \leq K}}} & (48)\end{matrix}$

Thus, for a transmitter with a pulse response of length L_(m) weidentify for this transmitter at source separation output [1] K vectorswhich are a linear combination of vectors [a(θ_(mp))^(T)h_(mp)(i) . . .a(θ_(mp))^(T)h_(mp)(i−L+1)]T dependent on the incidences θ_(mp) of themultipath of this transmitter.

Goniometry of the m^(th) Transmitter on the Vector u_(mk), 42,

The method then carries out, 42, a goniometry of a transmitter on one ofthe vectors u_(ml) . . . u_(mk) identified at source separation output.Under these conditions the vector u_(mk) is transformed into thefollowing matrix (49):${\underset{\_}{U}}_{mk} = {\left. \begin{bmatrix}u_{1} \\\vdots \\u_{N} \\\vdots \\u_{1 + {N{({L - 1})}}} \\\vdots \\u_{N + {N{({L - 1})}}}\end{bmatrix}\Rightarrow U_{mk} \right. = \begin{bmatrix}u_{1} & \quad & u_{1 + {N{({L - 1})}}} \\\vdots & \vdots & \vdots \\u_{N} & \quad & u_{N + {N{({L - 1})}}}\end{bmatrix}}$

According to the relation (48) U_(mk) is expressed by: $\begin{matrix}{U_{mk} = {{\sum\limits_{p = 1}^{P_{m}}{\rho_{mp}{\underset{\_}{a}\left( \theta_{mp} \right)}{\sum\limits_{i = 1}^{L_{m} + L}{\beta_{mki}{{\underset{\_}{t}}_{mp}^{L}(i)}^{T}\quad \text{such~~that}\quad {{\underset{\_}{t}}_{mp}^{L}(i)}}}}} = {\begin{bmatrix}{h_{mp}(i)} \\\vdots \\{h_{mp}\left( {i - L + 1} \right)}\end{bmatrix}}}} & (50)\end{matrix}$

The computer can then estimate the incidences θ_(ml) . . . θ_(mPm) ofthe paths of the m^(th) transmitter by applying a goniometry algorithmon the covariance matrix R_(mk)=U_(mk) U_(mk) ^(†), for example a highresolution algorithm such as MUSIC described in reference [3], authorsR. O. Schmidt, entitled “A signal subspace approach to multiple emitterslocation and spatial estimation”, PhD Thesis, Stanford University, CA,November 1991.

Identification and Elimination of Outputs u_(mk) (1<k<K) Associated withthe Same Transmitter, 43,

After performing the goniometry on the vector u_(mk), the computer willeliminate the vectors associated with the same transmitter i.e. theu_(mj) for j≠k. The matrices U_(m′j) associated with the u_(m′j) allsatisfy the following relation according to (50):

 U _(m′j) =A _(m′) B _(m′j) ^(T) with A _(m′=[) a(θ_(m′l)) . . .a(θ_(m′Pm′))]  (51)$B_{m^{\prime}j} = {{\left\lbrack {{\underset{\_}{b}}_{1j}\quad \ldots \quad {\underset{\_}{b}}_{{Pm}^{\prime}j}} \right\rbrack \quad {\underset{\_}{b}}_{pj}} = {\rho_{m^{\prime}p}{\sum\limits_{i = 1}^{L_{m} + L}{\beta_{m^{\prime}{ji}}{{\underset{\_}{t}}_{m^{\prime}p}^{L}(i)}}}}}$

Knowing that the projector Π_(m)=I−A_(m) (A_(m) ^(H) A_(m))⁻¹ A_(m) ^(H)satisfies Π_(m) A_(m)=0 we deduce that (52):

Cri(j)=trace{Π_(m) U_(m′j) (U_(m′j) ^(H) U_(m′j))⁻¹U_(m′j) ^(H)Π_(m)}=trace{Π_(m) P_(m′j) Π_(m)}=0

when m=m′

Where trace{Mat} designates the trace of the matrix Mat. For any matrixU_(m′j), the criterion Cri(j) is normalised between 0 and 1. When thematrix U_(mj) is associated with a vector u_(mj) associated with thesame transmitter as u_(mk) this criterion Cri(j) is cancelled. Knowingthat Π_(m) and U_(mj) are estimated with a certain accuracy, we willcompare Cri(j) with a threshold cc close to zero (typically 0.1) todecide whether the vectors u_(mk) and u_(m′j) belong to the sametransmitter: Cri(j)<α implies that u_(mk) and u_(m′j) are associatedwith the same transmitter and that m′=m. So to identify that a vectoru_(m′j) is associated with the same transmitter as the vector u_(mk) thecomputer performs the following operations:

1) After the goniometry on u_(mk) the computer determines the incidencesθ_(ml) . . . θ_(mPm) of the paths and builds the matrix A_(m) of theexpression (51). We deduce that Π_(m)=I−A_(m) (A_(m) ^(H) A_(m))⁻¹ A_(m)^(H).

2) it transforms according to relation (49) the vector u_(m′j) intomatrix U_(m′j). We deduce that P_(m′j)=U_(m′j) (U_(m′j) ^(H)U_(m′j))⁻¹U_(m′j) ^(H).

3) it calculates the criterion Cri(j)=trace{Π_(m)P_(m′j) Π_(m) } of theequation (52)

4) it applies for example the following association test:

Cri(j)<α u_(mk) and u_(m′j) are associated with the same transmitterm′=m and elimination of vector u_(mj).

Cri(j)>α m′≠m.

This operation is carried out on all different vectors of u_(mk), thenthe computer moves to the next transmitter, carrying out the goniometrystep on one of the vectors u_(m′j) not eliminated. After the goniometry,the method repeats the elimination and all these operations continueuntil there are no more vectors u_(m′j).

Estimation of the Delay Times of the Paths of the m^(th) Transmitter

According to an implementation variant of the method, the incidencesθ_(mi) of the P_(m) paths are known for 1<i<P_(m) and the associatedsteering vectors a(θ_(mi)) can be deduced. This information is used todeduce the propagation delays between the paths. To obtain the pathdelay values, the computer uses the outputs of the space-time sourceseparation. According to expression (2) we may write the expression (46)of y(t) as follows: $\begin{matrix}{{\underset{\_}{y}(t)} = {\begin{bmatrix}{\underset{\_}{x}(t)} \\\vdots \\{\underset{\_}{x}\left( {t - L + 1} \right)}\end{bmatrix} = {{\sum\limits_{m = 1}^{M}{\sum\limits_{i = 1}^{P_{m}}{\rho_{mi}\begin{bmatrix}{{\underset{\_}{a}\left( \theta_{mi} \right)}{s_{m}\left( {t - \tau_{mi}} \right)}} \\\vdots \\{{\underset{\_}{a}\left( \theta_{mi} \right)}{s_{m}\left( {t - L + 1 - \tau_{mi}} \right)}}\end{bmatrix}}}} + {{\underset{\_}{b}}^{L}(t)}}}} & (53)\end{matrix}$

We therefore deduce that the vectors u_(mk) according to expression (48)and the signals ŝ′_(mk)(t) obtained at source separation output andassociated with the m^(th) transmitter satisfy the following relation:$\begin{matrix}{{\sum\limits_{i = 1}^{P_{m}}\quad {\rho_{mi}\begin{bmatrix}{{\underset{\_}{\alpha}\left( \theta_{mi} \right)}{s_{m}\left( {t - \tau_{mi}} \right)}} \\\vdots \\{{\underset{\_}{\alpha}\left( \theta_{mi} \right)}{s_{m}\left( {t - L + 1 - \tau_{mi}} \right)}}\end{bmatrix}}} = {\sum\limits_{k = 1}^{K}\quad {{\underset{\_}{u}}_{mk}{{\hat{s}}_{mk}^{\prime}(t)}}}} & (54)\end{matrix}$

where ρ_(mi) designates the attenuation factor of the i^(th) path.Knowing that u_(mk) ⁰ corresponds to the first N components of u_(mk) wededuce that: $\begin{matrix}{{\sum\limits_{i = 1}^{P_{m}}\quad {\rho_{mi}{\underset{\_}{a}\left( \theta_{mi} \right)}{s_{m}\left( {t - \tau_{mi}} \right)}}} = {\sum\limits_{k = 1}^{K}{{\underset{\_}{u}}_{mk}^{0}\quad \cdot {{\hat{s}}_{mk}^{\prime}(t)}}}} & (55)\end{matrix}$

Expression (55) can be written in matrix form as follows:

 A _(m) s _(m)(t)=U _(m) ⁰ ŝ _(m)(t)  (56)

By putting: A_(m)=[a(θ_(ml)) . . . a(θ_(mPm))] and U_(m) ⁰=[u_(m) ⁰ . .. u_(mK) ⁰] and ${{\underset{\_}{s}}_{m}(t)} = {{\begin{bmatrix}{\rho_{m1}{s_{m}\left( {t - \tau_{m1}} \right)}} \\. \\{\rho_{mPm}{s_{m}\left( {t - \tau_{mPm}} \right)}}\end{bmatrix}\quad {then}\quad {{\hat{\underset{\_}{s}}}_{m}^{\prime}(t)}} = \begin{bmatrix}{{\hat{s}}_{m1}(t)} \\. \\{{\hat{s}}_{mK}(t)}\end{bmatrix}}$

Knowing the matrix A_(m) of steering vectors of the multipaths and thematrix U_(m) ⁰ of vectors identified, we deduce the vector s_(m)(t)according to the vector ŝ′_(m)(t) resulting from the space-time sourceseparation such that:

s _(m)(t)=A _(m) ⁻¹ U _(m) ⁰ ŝ′ _(m)(t)  (57)

Knowing that the i^(th) component of s_(m)(t) satisfiess_(m)(t)(i)=ρ_(mi) s_(m)(t−τ_(mi)) we maximise the following criterionto estimate the delay δτ_(mi)=τ_(mi)−τ_(ml) of the i^(th) path withrespect to the 1^(st) path. $\begin{matrix}{{{Cri}_{i}\left( {\delta \quad \tau} \right)} = {{{E\left\lbrack {{s_{m}(t)}(i){s_{m}\left( {t - {\delta \quad \tau}} \right)}(1)^{*}} \right\rbrack}\quad \text{such~~that}\quad \max \quad \left( {{Cri}\left( {\underset{\delta \quad \tau}{\delta}\quad \tau} \right)} \right)} = {\delta \quad \tau_{m\quad i}}}} & (58)\end{matrix}$

The method then executes the algorithm to estimate the δτ_(mi) for1<i<P_(m) consisting for example of performing the following steps:

Step No. 1: Construct A_(m)=[a(θ_(ml)) . . . a(θ_(mPm))] from incidencesθ_(mi).

Step No. 2: Calculate the signal s_(m)(t) using the expression (57).

Step No. 3: For each path perform the following operations.

Calculate the criterion Cri_(i)(δτ) of expression (58).

Maximise the criterion Cri_(i)(δτ) to obtain δτ_(mi)=τ_(mi)−τ_(ml).

Unlike the first method described above, in this case we use the Koutputs u_(mk) and ŝ′_(mk)(t) (1≦k≦K) of the space-time sourceseparation. In addition, we only use the 1st N components of u_(mk′).i.e. the vector u_(mk) ⁰(N number of antennas).

Simulation Example

In this example, we simulate the case of M=2 transmitters where one ofthe transmitters is composed of two paths. The two transmitters have thefollowing characteristics in terms of incidences, delays and paths:

1^(st) transmitter (m=1): composed of P₁=2 paths

such that θ₁₁=60° θ₁₂32 75° and the delay τ₁₁=0 τ₁₂=2 samples QPSK NRZwith 10 samples by symbols.

2^(nd) transmitter (m=2): composed of P₂=1 paths such that θ₂₁=150 anddelay τ₂₁₌0

FIG. 8 represents the MUSIC pseudo-spectra on the matrices R_(1i)(curveI) and R_(2i) (curve II) associated respectively with the first andsecond transmitters. The maxima of these pseudo-spectra can be used todetermine the incidences θ_(mp) of the multipaths of these transmitters.

What is claimed is:
 1. A method for space-time estimation of one or more transmitters based on signals received using an antenna network, said method comprising: separating the signals received using the antenna network to obtain signals s(t); grouping the signals s(t) by transmitter, said signals s(t) being from more than one transmitter; and determining an arrival angle θ_(mi) for each multipath p_(m) transmitted by each transmitter, wherein the grouping the signals s(t) by transmitter includes intercorrelating components of the separated signals.
 2. The method according to claim 1, wherein the intercorrelating includes intercorrelating two by two components u_(k)(t) of a signal vector s′ (t) resulting from separating the signals, and wherein the grouping the signals s(t) by transmitter further includes: finding one or more delay values to obtain a maximum value for an intercorrelation function, r_(kk′)(τ)=E; and storing path indices for which the intercorrelation function is a maximum.
 3. The method according to one of claims 1 and 2 further comprising: determining delay times using angles θ_(mi), a signal s_(m)(t), and searching for a maximum of a criterion Cri_(i)(δτ) to obtain δτ_(mi)−τ_(ml), with Cri _(i)(δτ)=E[s _(m)(t)(i)s _(m)(t−δτ)(1)*].
 4. The method according to one of claims 1 and 2, wherein P₁=P₂= . . . =Pm, where P_(m)=1.
 5. A method for space-time estimation of one or more transmitters based on signals received using an antenna network, said method comprising: separating the signals received using the antenna network to obtain signals s(t) by using a space time method before determining the arrival angles θ_(mi)for each multipath p_(m) of each transmitter; and comparing a signal s_(m)(t) to an output of a filter of length L_(m) before separating the signals, wherein said signals are from more than one transmitter.
 6. The method according to claim 5, wherein the signal s_(m)(t) is delayed for a given transmitter, and wherein the filter has inputs s_(m)(t) to s_(m)(t−τ_(m).
 7. The method according to claim 5 or 6, further comprising: identifying and eliminating outputs associated with a same transmitter after determining the arrival angles θ_(mi) for each multipath p_(m) transmitted by the same transmitter.
 8. The method according to one of claims 2 and 5, further comprising: using a MUSIC type high resolution goniometry method by interferometry.
 9. A storage medium for storing a computer readable program for space-time estimation of one or more transmitters based on signals received using an antenna network, said computer readable program comprising: a first computer code configured to separate the signals received using the antenna network in order to obtain signals s(t); a second computer code configured to group the signals s(t) by transmitter, said signals s(t) being from more than one transmitter; a third computer code configured to determine an arrival angle θ_(mi) for each multipath P_(m) transmitted by each transmitter; and a fourth computer code configured to intercorrelate components of the separated signals.
 10. The storage medium according to claim 9, wherein the fourth computer code is further configured to intercorrelate two by two components u_(k)(t) of a signal vector s'(t) resulting from the code to separate the signals, and wherein the second computer code comprises: a fifth computer code configured to find one or more delay values to obtain a maximum value for an intercorrelation function, r_(kk′)(τ)=E[u_(k)(t)u_(k′)(t−τ)*]; and a sixth computer code configured to store path indices for which the intercorrelation function is a maximum.
 11. The storage medium according to claim 10, further comprising: a seventh computer code configured to use a MUSIC type high resolution goniometry method by interferometry.
 12. The storage medium according to claim 9 further comprising: a fifth computer code to determine delay times using angles θ_(mi), a signal s_(m)(t), and to search for a maximum of a criterion Cri_(i)(δτ) to obtain δτ_(mi)=τ_(mi)−τ_(ml), with Cri _(i)(δτ)=E[s _(m)(t)(i)s _(m)(t−δτ)(1)*].
 13. The storage medium according to claim 9, wherein the first computer code and the second computer code are performed before the third computer code to determine the arrival angles θ_(mi).
 14. The storage medium according to claim 13, further comprising: a fifth computer code configured to compare a signal s_(m)(t) to an output of a filter of length L_(m) before the first computer code to separate the signals, wherein the signal s_(m)(t) is delayed for a given transmitter, and wherein the filter has inputs s_(m)(t) to s_(m)(t−τ_(m).
 15. The storage medium according to claim 13, further comprising: a fifth computer code configured to identify and eliminate outputs associated with a same transmitter after the third computer code to determine the arrival angles θ_(mi) for each multipath p_(m) transmitted by the same transmitter.
 16. The storage medium according to claim 9, wherein P₁=P₂= . . . =Pm, where P_(m)=1. 